I hear Recettear has a "New Game +" mode that becomes available after you beat the game. What are the differences between this mode and a first-time playthrough?
A New Game+ allows you to restart the game from the beginning, except that you keep many of the things you've already earned / unlocked. You get to keep:
You do not get to keep pictures, adventurers (unless you have their true cards), or shop expansions.
You get to keep all items in your inventory and the store from when you were when you won the game. Customers will retain their loyalty (and hence increased wallet size).
This is the same as simply loading your victorious save in "Endless" mode.
In addition, the adventurer you used the most in the previous game will give you their "True Card", which lets you hire them from the beginning (otherwise, you must re-unlock each adventurer, since you are effectively starting a new game, tutorial and everything). Since you only get one True Card per game (after you clear the total debt on week 5), NewGame+ is the only way to get the other True Cards, and thus complete the item encyclopedia.
Usually, these results combine to give a vastly easier game (just like losing).